When people say that you that you must eat meat to get all the nutrients you need, they are generally thinking of either B12 or Omega 3 fatty acids. B12 is only found in animal products. Omega 3 fatty acids are found in lots of common vegetarian foods, including tofu, but is not in a form that the body digests as easily as the form found in animal products.

The first thing to note is that these nutrients are only an issue for people who are fully vegan, and not just vegetarian. (Typically a vegetarian is defined as someone who eats no meat of any kind, and a vegan is someone who not only eats no meat, but also avoids animal products like eggs and cheese.) If you are a vegetarian for ethical reasons, the easiest way to be sure you get your B12s and easily digested Omega 3s is to find a source for eggs from chickens living in morally acceptable conditions.

Even for full fledged vegans, these nutrients don't have to be an issue. You can get B12 from vitamin supplements, which are fermented from bacteria, not taken from animals. And given how common foods with Omega 3s, including soy products and canola oil, are in vegetarian diets, I don't see that getting enough Omega 3s will be a problem for someone eating a healthy diet low in junk food.